Deep Inelastic Scattering in Conformal QCD

TL;DR

This paper develops a conformal field theory framework for analyzing deep inelastic scattering at small-x, using impact parameter representation and Regge theory, applicable to N=4 SYM and QCD, with exact results at weak coupling.

Contribution

It introduces a conformal impact parameter formalism for Regge limit scattering, connecting CFT correlators to impact factors and impact parameter space, and applies it to N=4 SYM and QCD.

Findings

Derived impact parameter representation for CFT correlators in the Regge limit.

Computed impact factors for N=4 SYM and QCD, revealing simple structures.

Confirmed the vanishing of the transverse spin 2 component for N=4 SYM R-current.

Abstract

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.